Thursday, December 23, 2010

Now that the offensive and moronic DADT policy has been repealed, it's time to revisit a Salon panel discussion held ten years ago.

Charles Moskos, the late Northwestern sociologist, tried to defend DADT by saying things like "That's just asking for trouble. How do we do it with men and women? It doesn't work there. We're having all kinds of cases, including as the women say, too many false accusations. Let's just muddle through the way we are with "don't ask, don't tell." It's much easier. I think the gender stuff is hard enough to deal with and to replicate that with sexual orientation just makes life too much trouble."

He also said, in Lingua Franca, that "I should not be forced to shower with a woman. I should not be forced to shower with a gay."

Your panel discussion on gays in the military was remarkable in that it did not even mention the experiences of other countries. Canada, for example, successfully integrated gays in the military some years ago, and the UK is now slated to follow the same path. Brigadier General Daniel E. Munro, the director general for personnel policy in the Canadian Forces, was quoted in the Washington Post as saying, "We would not have been able to prove that [homosexuality] had that deleterious effect on cohesion and morale that everyone talked about. Basically, we realized that we didn't have the evidentiary foundation ... It just wasn't there, I mean, you can't use the old cohesion and morale arguments just based on folklore. You have to be able to prove this stuff." If only U.S. military officials could speak with such honesty!

Wednesday, December 22, 2010

I have been having some of the strangest interactions I have ever had, with both Charles Lewis, religion columnist of the National Post, and Stephen Meurice, the Post's editor-in-chief. They resulted from my blog post reacting to Lewis's column, entitled Dear atheists: most of us don't care what you think.

First, Meurice. I asked him why it was acceptable to have Lewis's headline, but not acceptable to have the analogous headline with (say) "Jews" replacing "atheists".

I found his reply rather surprising. He thinks the distinction is that most Jews are born into their faith, while atheism is just "an opinion".

One great feature of both American and Canadian democracies is that we find discrimination against people for irrelevant attributes to be unacceptable. This principle is behind laws against employment discrimination, and the recent repeal of DADT. (Canada, I'm glad to say, ended discrimination against gays in the military long ago.)

But it is quite strange to suggest that discrimination against irrelevant attributes becomes unacceptable only when those attributes arise from the circumstances of one's birth.

If Meurice's view is correct, then we should be free to discriminate against adult converts to any religion. After all, the Jew who converts to Christianity was not born into his faith; he chose it, presumably after some intellectual struggle, and therefore, pace Meurice, it is just "an opinion". Similarly, we should be free to discriminate against adherents of new religions, such as Scientology or Branch Davidianism, since many adherents were not born into those faiths. This is clearly ridiculous.

Meurice's view also implies that if atheism becomes more mainstream - to the point, let's say, where most adherents are born atheists - then suddenly it would become unacceptable to discriminate against it. But isn't this the opposite of what should be the case? Established viewpoints don't need much protection; it's the more unfamiliar that routinely gets discriminated against.

So I don't think Meurice's distinction makes much sense.

Charles Lewis has also been corresponding with me - but in the oddest, passive-aggressive sort of way. At one point he wrote "I will never think of you again", but a few days later he was badgering me to publish this response on my blog. At another point he said he would call me to discuss a misunderstanding; when he finally did, he wouldn't let me speak, called me "weak-minded", and hung up in a huff.

The misunderstanding came about when I wrote a long response to some of his points, and even offered to buy him a coffee if he were ever in town. But he apparently didn't see that response, because he wrote back "you could have answered and created a dialogue". I've tried to resolve that, but he doesn't seem to want to listen.

If this is representative of the state of journalism in Canada, we're in deep trouble.

Thursday, December 16, 2010

I hadn't heard about convicted criminal Bob Enyart before, but based on yesterday's posting, I haven't missed much.

He gives a list of what he calls "typical atheist clichés" and then refutes them in a single line. Unfortunately, most of his "clichés" are straw men -- arguments that I've never heard, or rarely heard, anyone put forward, let alone atheists.

Let's take #1: "There is no truth!" Who ever said that, and what is it even supposed to mean?

Other of his "clichés" make sense, but only if you interpret them in a reasonable way. For example, #2 is "Truth is unknowable!" But the only sensible interpretations of that statement are (for example) that some truths are unknowable (which we know to be true from Gödel), and that other statements that we believe we know with certainty (such as our own birthdate) are, in fact, only held with justifiable and strong certainty, not irrefutable knowledge. Enyart's proposed rebuttal "How do you know?" is just nonsensical.

Enyart says "If your worldview can be dismantled within eight seconds, then get a better one." I'd say, if you think you have dismantled someone else's worldview in 8 seconds, you're just fooling yourself.

Wednesday, December 15, 2010

I wrote to Gordon Fisher, President of the National Post; Douglas Kelly, the Publisher; Jonathan Harris, VP of Digital Media; Stephen Meurice, the Editor-in-Chief; and Jonathan Kay, Managing Editor, Comment.

I asked them all the same thing: if it would not be acceptable for someone at the National Post to write a piece entitled "Dear Jews: Most of us don't care what you think", why is it acceptable for Charles Lewis to do so with "Jews" replaced by "atheists"?

Not a single person at the National Post was courageous enough to reply.

It speaks volumes, doesn't it, about the double standard that allows atheists to be criticized in the most vituperative and bigoted ways, with no uproar?

Sunday, December 12, 2010

I don't get that many creationists writing me, but I am indebted to a certain J. M. of Massachusetts, who has recently written to send me a copy of the November 2010 Jehovah's Witness publication, Awake!. He claims "This magazine points out some flaws in the atheists' reasoning."

Well, no, it doesn't.

The first article is entitled "Atheists on a Crusade", and is just one in a long line of articles by theists using religious language to denigrate atheism and evolution. "Called the new atheists," the article says, "they are not content to keep their views to themselves".

This just cracks me up. The Jehovah's Witnesses - you know, the folks who go door-to-door to spread their religion - are complaining because atheists are not content to keep their views to themselves. My irony meter just broke.

Another article, "Has Science Done Away with God?" repeats the canard that "everyday experience tells us that design -- especially highly sophisticated design -- calls for a designer". Well, no, it doesn't. That was resolved 150 years ago, when Darwin published The Origin of Species. We know now that mechanisms like mutation and natural selection can produce complexity and the appearance of design. The article goes on to ask, "What is the only source of information that we know of? In a word, intelligence". But anyone taking an introductory course in information theory at my university knows this is a lie.

It's a shame that creationists have to resort to untruths like this, but it's all they have.

Monday, December 06, 2010

It's hard to know what to make of it, other than that Lewis is terribly, terribly threatened by the rising popularity of atheism and atheist writers. He doesn't seem to know a damn thing about atheists, but believes they are all horrible, boring utopians.

As evidence of this, he trots out Christopher Hitchens and Richard Dawkins, and labels them "dreary". Hitchens, dreary? Lewis must be living in some bizarro universe where dreary means "vastly entertaining".

If I had to name a single famous person I'd love to have dinner with, it would be Hitchens, who knows much more about politics and history than I do, and is witty to boot. Dawkins would be a close second. Come to think of it, having them both for dinner would be perfect: Hitchens can talk about art, history, and politics, and Dawkins can talk about science.

I understand perfectly well why Lewis feels threatened by Hitchens. It was Hitchens who wrote The Missionary Position, exposing Mother Teresa as a pious fraud who loved poverty and suffering for everyone except herself. Lewis, who himself wrote on Mother Teresa, can't accept that characterization. But it is difficult to get a man to understand something when his salary depends on him not understanding it.

Lewis claims "most atheists do not have a clue what religion is about". Like most bigots, though, he doesn't present a shred of evidence for this claim. If he bothered to look at the evidence, though, he'd conclude just the opposite: atheists know more about religion than Protestants and Catholics.

Lewis gives North Korea as an example of a "godless society". But he doesn't dare mention the European social democracies, such as Denmark, Norway, and Sweden, all of which are good examples of peaceful, prosperous societies with significantly lower levels of religious belief than either Canada or the US. Nor does Lewis mention the behavior of officially religious societies, such as Afghanistan. That's simple dishonesty. Perhaps Lewis should review the Ten Commandments -- as I recall, there was this prohibition against "bear[ing] false witness".

Lewis claims "Atheists are under the ridiculous illusion that religious people think that all they have to do is call out to God and help will be on the way". Well, no. Atheists know that there is a huge variety of religious belief, and we also know that many Christians do believe exactly what Lewis says they don't. Pretending that this is not a large strain of North American religious belief is, simply, dishonest.

Lewis says "Faith is not up for debate". Well, I've got news for you, Chuck: you're wrong. In a free society, you don't get a pass because you call your beliefs "faith" and pronounce them off limits. Can't justify them? Fine with me. Just don't expect me, or anyone else to take you seriously.

I can just imagine the reaction if Lewis wrote a column entitled "Dear Jews: most of us don't care what you think". No doubt he'd be fired in a minute. But criticizing atheists is just fine.

Loren Graham, an American historian of science, and Jean-Michel Kantor, a French mathematician, have collaborated on a recent book, Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Harvard University Press, 2009).

Graham and Kantor's thesis is that a Russian religious cult, "name worshipping", was partly responsible for advances in set theory made by Russian mathematicians in the early 1900's, whereas the French "rationalistic, Cartesian" approach prevented similar breakthroughs. Indeed, on p. 189 they claim "under the influence of their [Borel, Baire, Lebesgue's] ultra-rationalistic traditions, they lost their nerve". (However, this supposed "loss of nerve" is not supported by any documentation.)

I found it an interesting book, but one that did not successfully support its thesis. After all, placing the responsibility for an historical event on some other single event or belief is highly problematic: consider that there are still people who debate the conclusion that slavery was a primary cause of the American civil war. Why one group solved a mathematical problem, while another failed, is not always so simple to determine. It can be a matter of pure intellectual ability, or a desire to focus on one area rather than other, or something entirely random, like a conversation in a café. Graham and Kantor hedge a bit on p. 100, where they write, "when we emphasize the importance of Name Worshipping to men like Luzin, Egorov, and Florensky, we are not claiming a unique or necessary relationship. We are simply saying that in the cases of these thinkers, a religious heresy being talked about at the time when creative work was being done in set theory played a role in their conceptions. It could have happened another way; but it did not." But if this all they were saying, then so what?

Srinivasan Ramanujan believed that his family's deity, Namagiri, whispered equations in his ear. But it doesn't necessarily follow that without a belief in Namagiri, he would not have created the mathematics he did. Maybe he would have been an even better mathematician had he not been imbued with his Hindu superstitions.

Similarly, it's not clear to me that Russian mathematicians like Egorov, Luzin, Florensky, and others could not have been just as successful -- or even more so -- had they not subscribed to their bizarre Christian cult. It even seems that their cult could induce ridiculous statements like the one the quote from Bely: "When I name an object with a word, I thereby assert its existence." That will certainly be news to unicorns and the set of all sets. Similarly, Luzin wrote that he "consider[ed] the totality of all natural numbers objectively existing" (italics in original), which raises the question, what precisely does it mean for a number to "exist"? This point is not really discussed by the authors. But it seems to me that, for example, that the number ℵ0 "exists" in exactly the same way that the number 4 "exists".

The book is generally well-presented, although I found a couple of things to quibble about. On page 58, for example, the authors claim that "explicit namings of even one of them [normal numbers in base 10] have been very difficult to obtain". But this is not true. For example, Champernowne's number .123456789101112 ..., which consists of the decimal expansions of the integers concatenated in increasing order, has a very simple proof of normality found by Pillai in 1939. Many, many other examples are known, such as the result of Davenport and Erdős in 1952 that .f(1)f(2)f(3)... is normal if f is any polynomial taking positive integer values at the positive integers. And I was also annoyed by the misspelling "Riemanian surfaces" on p. 113 --- "Riemann" has two n's, not one --- and the failure to put the proper accents on Wacław Sierpiński on p. 118.

Nevertheless, this is a little book worth reading, even if its main thesis is poorly supported. For me, the best part of the book was the history of Soviet mathematics in Chapters 7 and 8. Although I knew the names of most of the Russian mathematicians discussed, I had not explicitly realized the extent of mathematical talent in Moscow in the 1920's. And the mistreatment of Egorov, Luzin, and Florensky under Communism, and the bravery of people like Chebotaryov who stood up for them and suffered as a result, is a cautionary tale worth knowing about.

Saturday, November 27, 2010

William Lane Craig seems, for some reason that I've never understood, to garner disproportionate respect from theists and even some nontheists. (But then, I'm also mystified by the cult around C. S. Lewis, who seems to me to be a sloppy and childish thinker.)

Take a look at this debate entitled "Does the Universe have a purpose?" and see if Craig lives up to his reputation. Of course, in debates, where there is a limited time, we are all forced to simplify our statements, so perhaps Craig doesn't really believe exactly what he is saying. Nevertheless...

In his opening statement (jump to 13:41) , he piled false claim upon false claim. For example:

"If God does exist, then the universe does have a purpose." Really? That doesn't follow. Just because an intelligent being makes a thing X, that is insufficient to show that X has a purpose. After all, I could pick up a couple of rocks aimlessly at the seashore and put one on top of the other. What would be the purpose of that pile of rocks? Perhaps there is none at all.

"According to Biblical theism ... The purpose of life is to be found in a personal relationship with a holy and loving God. As the Westminster catechism asks, What is the chief end of man? To glorify God and enjoy him forever." Huh? This was a non sequitur. The subject of the debate was whether the universe had a purpose, not the purpose of life or man.

Craig relied upon a false dichotomy - the only two choices he presented are "Biblical theism" and "atheism". But these are clearly not the only possibilities. Why couldn't the Universe have been made by a nasty and childish god, who delights in tormenting us in new and ingenious ways? Maybe the purpose of the Universe is to amuse this god with our suffering. Or perhaps there are multiple gods, each wagering on our behavior when confronted with new diseases or painful medical procedures.

"God gives an objectively purposeful life." Not true, since we have no objective way to determine this purpose. Craig think the purpose is spelled out in his holy book. Another might say the purpose is spelled out in a different book. We have no objective way to determine which is correct... or maybe they're all wrong. Maybe a god designed our universe for the purpose of making atheism the single world belief.

"What is evil? - I maintain that evil is a departure from the way things ought to be..." Let's look at the sensibility of this definition. Perhaps I think the way things "ought to be" are that we should all have jet cars and live on Mars. Since the current state of affairs is different from the way things "ought to be", using Craig's definition I would have to say the current state of affairs is "evil". But this would not be assented to by most people who use the word "evil". Yet if I say, "Hitler was evil", this would be assented to by most people. So Craig's definition does not capture the way most people use the word "evil".

"If there is a way things ought to be, then there must be some transcendent design plan or purpose that determines how things ought to be. And so there must be some transcendent being - a Creator in fact - whose will is the basis for how things ought to be. And so evil is actually evidence that God does exist." This doesn't follow at all. Why could not a sense of "the way things ought to be" be the product of biological evolution?

And to top it all off, this was delivered with a kind of wheezy smugness out of proportion to the quality of the arguments. Bleh.

Monday, November 22, 2010

If philosophers think the view that "The brain is not an organ of consciousness. … The brain has no cognitive powers at all" deserves anything more than a good horselaugh, this simply shows how irrelevant philosophy has become.

Our future understanding of cognition will come from neuroscience, not from Wittgenstein.

Friday, November 19, 2010

Just when you thought he couldn't get any weirder, here is the crackpot Turkish creationist Harun Yahya (pseudonym of Adnan Oktar) blaming 9/11 on the CIA, and "deviant Arab communists, Darwinists, and materialists".

Of course, anyone who has studied the incident knows that in fact the 9/11 attackers were pious Muslims who worshipped at mosques like al Quds in Hamburg and spent much of their time talking about religion. There is simply no indication at all that they knew a damn thing about evolutionary biology or Darwin.

Yahya isn't much different from the theocrats at the Discovery Institute, who want to link Darwin to both fascism and communism.

Sunday, November 07, 2010

Those creationists are just so darn cute when they try to do mathematics, you just want to pinch their cheeks.

Here's Robert Sheldon, who babbles about infinity so incoherently, the folks at Uncommon Descent thought they should reprint it for all to see. And what a mess it is.

Despite claiming that he's "gotten quite comfortable with infinity", he emphasizes that "the important thing is not to think about it too long". And that is certainly what he's done!

How many errors can you spot in this word salad? This is a good one: "For example, take the number line from 1 to ∞. It’s infinite of course. But now divide every number by the largest number on the line." Yeah, that'll work really well.

And here's another: that the cardinality of the irrational numbers is denoted ℵ1. I guess Mr. Sheldon has never heard of the continuum hypothesis.

I think Mr. Sheldon and Marvin Bittinger should get together. What a great book they could write!

Monday, November 01, 2010

Call for papers: A special issue of Journal of the Australian Mathematical Society dedicated to Alf van der Poorten.

We solicit submissions in all areas of mathematics, and especially in the areas close to the research interests of Alf van der Poorten (e.g., recurrence sequences, continued fractions, diophantine approximation, and p-adic numbers). The submission deadline is 1 May 2011. We hope to have all submissions evaluated and make the acceptance/rejection decision by th end of October 2011 with the goal to have this issue to appear early 2012.

Friday, October 22, 2010

I was once arguing with Eugene Volokh about the separation of church and state in the US. From his lawyer's perspective, he thought the really important issues at the church-state boundary concerned things like "parochiaid" - direct or indirect aid to religious schools - and probably most legal scholars agree with him.

But from my point of view, the really important issues concern things like "In God We Trust" on money, and "under God" in the pledge of allegiance. These seem trivial to people like Volokh, and they're often dismissed as "ceremonial deism". For example, in Lynch v. Donnelly, 465 U.S. 668, Justice Brennan (dissenting) wrote "such practices as the designation of "In God We Trust" as our national motto, or the references to God contained in the Pledge of Allegiance to the flag can best be understood, in Dean Rostow's apt phrase, as a form a "ceremonial deism," protected from Establishment Clause scrutiny chiefly because they have lost through rote repetition any significant religious content".

But now go read this article about Christian prayers broadcast over a loudspeaker at football games at Soddy Daisy, a public high school, in Tennessee. This is a pretty clear violation of separation of church and state, right? Now look at what one local parent, Jim Rogers, uses to justify the practice: "Our country was founded on the principle of religious suffrage and the freedom to express that religion. They incorporated God into our money, the oath of office, our legal system, the Pledge of Allegiance. You cannot find one aspect of our secular government that doesn’t make reference to our creator."

Mr. Rogers clearly doesn't know a damn thing about the separation of church and state, and I doubt he could explain what "ceremonial deism" is. But he does know something that Prof. Volokh doesn't: small, creeping violations of separation have a lot of symbolic value. Rogers knows damn well that having "In God We Trust" on coins is full of "significant religious content".

Lawyers love to say De minimis non curat lex. But the average person knows that when school children are coerced every day into saying "one nation, under God, indivisible", this is more than just "minimis". That's why people in favor of separation need to speak out against the smallest violation. Every crack in the wall just leads to more cracks.

Of all the bogus claims promulgated by evangelicals, one of the most pernicious surely has to be the implication that Republicans are morally superior.

Yes, in the 19th century the Republicans were against slavery - and at a time when many evangelicals were for it (something conveniently omitted by Reynolds -- see, for example, Daly's book, When Slavery was Called Freedom). Yet it is hardly possible to maintain that the Republican party of the 21st century is the same party. Heck, the Republicans abandoned black people only 11 years after the Civil War ended, with the Compromise of 1876. Seventy years later, we were treated to the spectacle of the Republican Eisenhower testifying against integrating the military.

The Republicans are now for "freedom of thought"? Hardly possible to maintain with a straight face - read The Republican War on Science. Republicans are, in general, far more censorious than Democrats - although the Demos have their problems, too.

Republicans are "are hesitant to make any person do good by the force of law"? Truly laughable. Republicans are at the forefront of those wanting to prevent gays from adopting and teaching in schools.

By all means, vote Republican if you think they're going to do a better job. But don't pretend moral superiority that doesn't exist. Reynolds' essay is a bad joke.

Monday, October 11, 2010

I just received the sad news that my friend and colleague, Alf van der Poorten, passed away on Saturday in Australia.

Alf (or "vdp", as he was sometimes called) specialized in number theory, and he wrote about 170 papers on the subject, specializing in continued fractions, elliptic curves, transcendence, Diophantine approximation, and recurrence sequences. He had dozens of co-authors, and he especially liked to write with his Macquarie colleague John Loxton and with Bordeaux mathematician Michel Mendès France. Alf wrote a book, Notes on Fermat's Last Theorem, which was published by the CMS in 1996, and was co-author (with Everest, Shparlinski, and Ward) of another, Recurrence Sequences, published by the AMS in 2003. We had vague plans to write a book together on continued fractions, but we never did. We did, however, write four papers together.

Among number theorists, Alf was an "original fini", as the French say. His talks were often accompanied by transparencies lettered in Alf's distinctive hand, full of quotations and puns. (A book that he co-edited in honor of the computational number theorist Hugh Williams was called High Primes and Misdemeanours.) Some of his papers contained limericks -- and not always in good taste! One of his most-cited papers was just called "Folds!". He loved the mathematical typesetting system TeX passionately, and developed a large set of his own arcane macros, which sometimes made collaboration difficult.

Alf was born during World War II to Jewish parents in Holland who gave him up to another family to protect him from the Nazis. But they all survived the Holocaust, and Alf was reunited with his parents after the war. They moved to Australia around 1950, and Alf got a Ph. D. in mathematics from the University of New South Wales in 1968. He taught at Macquarie University for many years, and, after retirement, ran his own Centre for Number Theory Research out of his home in suburban Sydney. Alf spoke English with a distinctive mix of both Dutch and Australian accents. More information about his life can be found here.

Alf and his wife Joy welcomed me during my only visit to Australia back in 1991. I spent a month living on the campus of Macquarie University and working with Alf on continued fractions. One of the papers we wrote concerned the continued fraction expansion of numbers such as 2-1 + 2-2 + 2-3 + 2-5 + 2-8 + ..., where the exponents are the Fibonacci numbers. Working with Alf was a lot of fun. He would gesture languidly in the air with a cigarette-laden hand, moving quickly from topic to topic: Australian politics, other mathematicians he had known, an idea for our latest proof. Alf knew a lot about many different subjects and had a quip or story ready for almost anything. He had phenomenal mathematical intuition and nearly always found the right path to a solution, but he wasn't always rigorous when he wrote up his results. One of his celebrated papers, about the transcendence of automatic numbers, contained a serious flaw which he was never able to repair.

Alf travelled a lot. We worked together at Dartmouth College, and later, when I moved to the University of Waterloo, he came for one of the CMS meetings. During one of his visits, he told me about his clogged arteries. He had been walking along when suddenly he found himself unable to speak. He sat down on a bench and was taken to the hospital, where it was found that an important artery was nearly completely blocked. After surgery he made a full recovery and continued to do mathematics. More recently, he had surgery for cancer of the lip (where a cigarette had always rested in the past) and eventually developed the brain cancer that killed him. At one of the CMS meetings dozens of mathematicians signed a card for him.

Alf was active in the number theory community and served as president of the Australian Mathematical Society from 1996 to 1998 and won several awards, including the George Szekeres medal. I will miss him.

Tuesday, September 21, 2010

Here is a neat trick that lets you avoid initializing large arrays. I learned about it long ago from Aho, Hopcroft, and Ullman, The Design and Analysis of Computer Algorithms, an old but still great book — but I think it is probably an old hacker's idea.

To illustrate the idea, suppose we are trying to solve the element distinctness problem on a restricted universe. In this problem we are given a list of integers and we want to determine if there are any repeated elements. The input is an array A[1..n] of integers, where each integer is between (say) 1 and M, where M is not so large compared to n — maybe M is about 10n or something like that.

The usual way to do this is to create an array B[1..M] such that B[j] = 1 if j is an element of A, and 0 otherwise. We start by initializing all the entries of B to 0. Then we loop through the elements of A. For each i, 1 ≤ i ≤ n, we first check B[A[i]]. If it equals 1, then the value A[i] already occurred in A. Otherwise, we set B[A[i]] := 1, to signify that we've seen A[i].

If M = O(n), this gives a linear-time algorithm for element distinctness. It even lets us list the repeated elements, if there are any.

Now here's the deal. Suppose we are solving element distinctness many times in a program, as a subroutine. Then it is conceivable that initializing all the entries of B to 0 could actually be a significant time drain. Although we have to allocate the memory for B once at the start, could there be a way to avoid the time-consuming Θ(M) initialization for B each time we call the subroutine again? We have to handle the problem that the entries of B could be arbitrary junk that we have no control over.

The answer is yes, using the following trick: instead of containing 1 or 0, we will set it up so that B[j] contains the position p in A where j is found. The key point is that we always actually verify this by looking at A[p], so we can never go wrong, even if B[j] is junk. More precisely, we want to ensure that if B[j] = p, then A[p] = j.

Now for each i we are going to check to see if A[i] = d has already been seen. To do this, we look in B[d]; say it equals c. If c is not between 1 and i-1, then we know that c represents uninitialized junk, so we can confidently ignore it and set B[d] = i.

If c is between 1 and i-1, then it either represents a true pointer back to the place in A where d was found earlier, or it just happens to be junk that is in the right range. In either case, we look at A[c]. Either it equals d, in which case we have found d earlier in the array at the entry A[c], or it equals something else. In the latter case we also set B[d] = i. This works whether B[d] is a true pointer or not!

And that's it! This code fragment prints out the duplications. Of course, if you'd rather terminate as soon as a repeated element is found, you can do that instead. Or if you'd rather save the repeated elements in a linked list, you can do that, too. And of course, this trick can be used in other settings, such as large sparse matrices, where you want to avoid initialization costs.

Monday, September 20, 2010

Over at the creationist "Leadership University" site, Doug Groothuis has a piece called "Six Enemies of Apologetic Engagement", where he lists some ways that evangelical Christians fail to carry out their mission effectively.

It's a real hoot. "Ignorance" is one of the enemies, but Groothuis also makes the bogus claim that "macro-evolution is false, and good arguments have been raised against it from both nature and Scripture". He actually cites the vastly-ignorant Phillip Johnson -- a lawyer with no training in biology -- as someone who has made good arguments with "intellectual integrity" against evolution. (Groothuis also misspells Johnson's first name.)

I remember the time that Phillip Johnson arrived at the Usenet newsgroup talk.origins, back in 1993. He arrogantly rode in on his evangelical high horse to do battle with the godless evolutionists, confident that his rhetorical skills would hide his lack of biological knowledge. The result was not pretty at all. Johnson had to leave in a cowardly huff because he couldn't handle the criticism from people who actually knew something about the subject.

"Cowardice" and "arrogance", however, are two of Groothuis's problems with evangelicals. He says that evangelicals should "cultivate real dialogue with unbelievers". Is that the very same Doug Groothuis who routinely bans commenters at his blog who disagree with his claims? Why, I believe it is.

Tuesday, September 14, 2010

Here's a poem by Hooper Reynolds Goodwin that was published in the journal Scripta Mathematica in 1953. I liked it very much when I was a teenager, and I still think the last two lines are excellent.

PARABOLA

This curve I'm plotting? A parabola. This point is called the focus; it's the point—Oh, no, not an ellipse. Ellipses have two foci: Here, I'll show you one I've drawn. You see the difference. These two lines of the parabola, They stretch out wide and wider, "World without end," as preachers say. (I don't know what they mean; perhaps they don't); But you see how it goes.

There was a man—Sir Isaac Newton, I believe it was— Who had the notion a parabola was an ellipse, Its other focus at infinity. You may not understand just what he meant; You have to sort of take the thing on faith. The keenest scholar can't quite picture it, you know.

I've often thought, It might be called a symbol of man's life; A curve of ever-widening sweep. And here in this world Is the focus we may call, say, temporal interests, Food and drink and clothes . . . But yet it cannot be that this is all; For out beyond the reach of sight must be Another point, a heavenly focus, see? 'Round which the sweeping curves of human life Complete the ellipse. Fantastic? Well, perhaps, But yet the more I think of it...

And here— Another thing I've often thought about: Suppose we draw here two parabolas With axes parallel, and let the arms cross— "Intersect" the word is—at this point. Now if there be a focus Somewhere out beyond the bounds of space, And these are two ellipses, As Sir Isaac thought they were, Why, don't you see, they'll intersect again Somewhere out there. Just as two lives that once have crossed, Then gone their separate ways, And one has disappeared long since into the void of death May—but who knows? It's just a thought...

Well, come again; I don't get callers often. They don't see much in old folks nowadays, And when a man's not only old, but got his head Stuck always in a book of "AnaIyt!" Young people think I'm queer; they can't see why A man that doesn't have to study graphs Should plague his head; don't understand that such Dry, dull things as a parabolic curve May bring up mem'ries of a face that's gone.

The author, Hooper Reynolds Goodwin (December 5 1891-October 13 1964), was born in Marblehead, Massachusetts. Raised by Unitarians, he attended Boston University and was ordained as a Methodist minister. Later he became an Episcopalian minister. He served in churches in Bethel and Randolph, Vermont.

I am very grateful to his granddaughter, Sue Maltais, for providing a photo and information about his life.

Wednesday, September 08, 2010

My sabbatical is over and it's back to a teaching term. Classes start next week.

Here's what I'm doing today (with updates throughout the day):

5:30 AM Woke up, had breakfast, and started answering e-mail. Hey, the Phillies are in first place in their division! I worked on processing mail for the journal I edit, the Journal of Integer Sequences.

7:40 AM The kids are off to school - both of them are now in high school! (urk)

8:30 AM Arrived at work. I'll be teaching a multi-section course on algorithms. I'm teaching two sections, with 60 students each, and another instructor is teaching the third -- so there's a lot of coordination to do. I sent e-mail to the other instructor with some suggestions about the first two assignments. I found my book of notes and overhead slides from the last time I taught the course. Some things I can reuse, but other things I will revise.

8:50 AM Time for coffee! While I was gone, we got an espresso machine. I don't like the taste, though -- the coffee machine at Oberwolfach was much better. The one here at Waterloo makes coffee that's way too bitter for me.

9:00 AM Damn, the radio feed from WBUR is acting up, so listening to the news is painful. I switch to the BBC radio program "Newshour".

9:10 AM There's a really interesting article by Lionel Levine and Jim Propp in the latest issue of the Notices of the AMS, on sandpiles. I'll have to think about this stuff more when I get a chance.

9:28 AM Noga Alon is visiting Waterloo, so I sent him an e-mail message asking if he would have a few minutes today or tomorrow to discuss a problem.

9:30 AM Working on the first assignment for my algorithms course. It's not easy to create good, interesting problems about big-O notation. And I want problems whose solution isn't on the web! I had a good one last year but I don't want to reuse it.

10:15 AM Got a couple of problems written, but still looking for a really hard one. Time to go check my (physical) mailbox on the second floor. Most mail comes electronically these days, but still...

10:35 AM OK, I have a draft of the first problem set done. Not completely happy with it. Sent it off to the other instructor for his comments. Noga Alon says he'll be in soon. Now - time to answer some e-mail.

11:20 AM E-mail! It's the bane of my existence. I get lots of messages a day, and don't know what to do with all of them. Best is a message that requires little thought and demands an immediate response. Worst is somebody asking a question that I'm not quite sure how to answer. I don't answer and it gets buried, perhaps never to emerge again. My mailbox always has hundreds of messages and is slow to load. Wish I could get it better organized.

Eating lunch while working. I always get hungry around 11 AM and it's hard to resist eating lunch early.

11:50 AM A colleague from another country was denied a visa to visit Canada and present a paper at a conference. This is really outrageous. I've got an appointment with my MP next week to discuss this case. I'm printing out the documentation that the colleague sent me.

12:00 Noon There's a new version of the APL I use on my mac, APL X. Paid $160 Canadian for the update through paypal.

12:30 PM Spent the last half hour trying to submit a paper to Information Processing Letters. Gone are the days when you could submit a paper by e-mailing some files to the editor. Now you have to go through a web-based form where you attach files, etc. These nearly always are terrible, offering way too many options for some things and not enough for others. I've spent 30 minutes on it so far and am still not done.

12:45 PM Whew! Submission finally done.

12:50 PM Got passcode for new version of APL, and installed it. Seems to work OK.

1:00 PM A colleague once suggested trying to find examples of k-tuples of integers S where g0 (S) > g1 (S) > g2 (S), where gi (S) is the largest integer having exactly i representations as an N-linear combination of the elements of S. Ran my little APL program and found the example S = (40,46,59,61,92), where g0 = 373, g1 = 354, and g2 = 340. It would be interesting to show there are arbitrarily long descending chains like that. Do you need larger and larger k-tuples to get them?

1:20 PM Went down to the visitor's office to try to find Noga Alon, but didn't find him.

1:25 PM Worked on the algorithms course web page.

1:35 PM Off to the grad course info session to present information about my Winter 2011 course on formal languages.

1:55 PM Back from the course presentation.

2:00 PM Noga Alon kindly came by and we talked about the separating words problem. At the same time our local computer people came by and tried to figure out why Thunderbird has lots of problems with my mail. Chaos!

3:30 PM Department meeting - free cookies. We learned about a new draft policy on privacy at the university, which as currently drafted would have the unfortunate effect of preventing professors from archiving things like student project for more than one year. This would make writing recommendation letters difficult in many cases. I certainly hope this draft policy will be rewritten.

Friday, September 03, 2010

Wow, Doug Groothuis has banned me from his blog for writing the following, which he refused to publish:

I think this excerpt shows why, for non-Christians, C. S. Lewis's philosophy is regarded as deficient.

Lewis didn't know anything about evolution. He didn't understand that what he called "morality" is a fact about human evolution; that we are programmed by evolution and culture to regard certain behaviors of others as acceptable and other behaviors as less so. Once this is understood, Lewis's confusion simply vanishes.

He calls this "pugilistic, pugnacious, and pernicious propositions."

Students of Groothuis should be aware: he does not tolerate any kind of dissent. If I were you, I'd look for another teacher, one that respects the give-and-take necessary to acquire knowledge.

Monday, August 30, 2010

We have our home internet service through Rogers. While it usually works reasonably well, when it doesn't, it is really hell trying to go through Rogers customer service.

Here's what happened this weekend. I arrived home, back from Oberwolfach, and our internet service was down. So we tried to call Rogers 24-hour line for internet problems. However, their voice mail menu was also acting strangely. First, it asked me to enter the digits of my postal code, and when I did this, it then said "That was not a valid response." After a second go-round, it then connected me with the Rogers credit department -- not the Internet problem line -- which then provided the helpful message "The Rogers credit department is now closed. Please call back during regular business hours".

Pushing 0 at any point did not help. Either it said "That was not a valid response", or it transferred me to the credit department. We tried over and over again, trying to enter different numbers, etc. We also called other Rogers numbers. Nothing worked.

We eventually got through by calling Rogers from a different phone. So somehow it is recognizing my home phone number and then acting strangely.

Then this morning I tried to explain to Rogers that their voice mail was not working. What a waste of time that was! They seemed completely uninterested in the fact that it is badly broken, and several people I spoke to did not even believe it. Nor are they willing to give me a call when it is fixed. So here I am with no internet and no direct way of calling Rogers from my home phone to report it!

Still not convinced? How about the way they handle distribution of the iPhone 4? Since I'm back from a sabbatical in the US, I'm in the market for a new cell phone. Rogers had a website where you could sign up for iPhone 4 updates. But then it arrived in stores with no notification to me. And now, if you want one, there's no waiting list you can join. If you want one, you just have to show up at a store when they open, hoping this will be your lucky day. There's no rational basis for this kind of crappy product distribution.

How does such a billion-dollar company survive with such lousy customer service?

For mathematicians, it's a little bit like Mecca for Muslims: everybody wants to go at least once in their lifetime.

I first heard about Oberwolfach when I was an undergraduate. My first significant paper had finally appeared in the Journal of Number Theory after a very long delay (that's another story), and I sent it off to some mathematicians I thought would be interested. One replied, "But I just heard Schinzel talk about this at Oberwolfach..." I had been scooped! During the long delay in publication, a Czech graduate student studying in Poland had found the same result. And what was Oberwolfach?

For those who are not familiar with what happens at a place like Oberwolfach, here's a brief account. For 50 out of 52 weeks of the year (the exceptions being Christmas and New Year's), the Institute is host to about 50 mathematicians who arrive from Germany, the rest of Europe, and around the world. Each Sunday, they typically arrive by train at either Hausach or Wolfach, two small towns in a river valley in mountainous southern Germany. From there they take a taxi to the Institute, which is located on a remote tree-covered hillside that's a good 5 km from the nearest town.

There are two main buildings. One houses the dormitory and cafeteria, the other the library and conference rooms. Oberwolfach provides three meals a day; at lunch and dinner there is assigned seating, which changes at each meal. The main work takes places Monday through Friday, and usually consists of some talks (we had about 4 hours each day) and working on problems in small groups (all the rest of the day and night). There are numerous coffee machines (Paul Erdős supposedly once said that "A mathematician is a machine for turning coffee into theorems", although it has also been attributed to Rényi), where espresso and café au lait can be had, gratis, at all hours. Drinks, both alcoholic and non, can be bought for very nominal prices. The picture below shows the result after a long night of drinking and mathematics.

The dormitory rooms are very spartan, with no decorations and no TV, radio, or phone. Although there is some wireless internet available in both buildings, most dormitory rooms do not have access. You're supposed to be talking to other mathematicians, not sitting in your room!

I was there for a "mini-workshop" on Combinatorics on Words. We had 17 participants, and there were two other workshops running concurrently. This differs from most weeks, which are typically devoted to a single theme and involve more participants.

Oberwolfach also offers other kinds of programs, such as "Research in Pairs", which allow two mathematicians from different institutions to meet and work together for a longer period.

The library is really outstanding. Unlike many libraries, they have not switched to electronic subscription, and they continue to receive paper copies of journals. It is a real pleasure to walk down the long aisle and pick up a journal to browse. Although I thought I knew the mathematical literature reasonably well, there were still some journals I had never heard of.

Oberwolfach also has a tradition of putting books written by participants on a special shelf in the library building. You can see my book displayed there below.

Another Oberwolfach tradition are the problem books. Any mathematician can provide an unsolved problem, or comment on a previous one, and there are dozens of problems by famous mathematicians like Erdős. Here's a page from the problems book with a problem by Mendès France:

On Saturday, all the mathematicians leave in taxis arranged by the Institute. And on Sunday the cycle begins again.

I had a really great experience there. There were some excellent talks by my colleagues, and I got a chance to discuss some open problems with them. We even solved one problem, and made some progress on others. I'm hoping to go again some day!

Thursday, August 19, 2010

I was very sad to learn this morning that my old friend and colleague, Gene McDonnell, died on August 17.

Gene was actively involved in the development and promotion of APL. He was one of the first people I met when I worked at the IBM Philadelphia Scientific Center, and he later hired me to work for I. P. Sharp in Palo Alto.

Gene had a wide variety of interests. He could talk knowledgeably about mathematics, science and literature, and he had a playful sense of humor. He wrote a beautiful paper entitled "Complex floor", which gave an entirely new way to generalize the familiar greatest integer function (or "floor") to the complex plane. As an undergraduate, I wrote my thesis on his extension, showing that you could use it to define continued fractions for complex numbers -- though there are still questions unresolved about that!

Gene and I wrote a paper together entitled "Extending APL to infinity", which suggested some ways of adapting the computer language APL to the extended real numbers. We also made a proposal to extend APL to infinite arrays, basically involving some lazy evaluation schemes. As far as I know, nobody ever implemented our ideas, although I still think it would be interesting.

Gene wrote a series of excellent columns for APL Quote-Quad (now sadly defunct) entitled "Recreational APL". For many of us, it was the first thing we turned to when the new issue arrived. I remember in particular one beautiful column about leap years that inspired a paper I wrote, "Pierce expansions and rules for the determination of leap years", in 1994.

Gene was intellectually active up to his last days. The most recent message I received from him was in April, where he proudly announced the publication of his new book, At Play With J, a compendium of his columns from Vector, the British APL magazine.

I'll remember Gene for his bright blue eyes, his warm and engaging smile, and his intellectual achievements. Farewell, old friend.

Whatever happened to good science reporting? The supposed effects form a classic list of vague symptoms that are likely to have a psychosomatic component: headaches, dizziness, nausea, racing heart rates. A good reporter should be more skeptical.

The article cites Susan Clarke, "a former research consultant to the Harvard School of Public Health", as claiming that Wi-fi "alters fundamental physiological functioning and can cause neurological and cardiac symptoms". But the article doesn't bother to quote any medical official or researcher to the effect that Wi-fi is safe. Nor does it cite any peer-reviewed studies by Clarke or anyone else on the subject.

Really, a little common sense would be useful here. With Wi-fi available in libraries, cafes, airports, and so forth, for years, wouldn't everybody be reporting these supposed effects?

Friday, August 06, 2010

Religion reporting seems to attract some of the very worst elements of the journalism profession. Some, like my local paper's Mirko Petricevic, have never met a religion they didn't like; they never ask a single hard question of a believer. Others, like NPR's Barbara Bradley Haggerty, apparently view their profession as a means to convert others to their religion. (She's a member of the World Journalism Insititute, whose goal is "to recruit, equip, place and encourage journalists who are Christians in the mainstream newsrooms of America first and then the world.")

Haggerty's at it again, with a story about how academia supposedly discriminates against religious conservatives.

Unfortunately, her poster child is Mike S. Adams, a first class looney-tune who has called for "atheist-haters" to join atheist student groups at universities and hence destroy them. Poor Mike S. Adams, who was discriminated against by getting tenure at his university.

Thursday, August 05, 2010

Here's a commentary from the Asian Tribune by Habib Siddiqui, decrying the backlash again the proposed Cordoba Islamic Center in New York City. Shame on those bigots!, he concludes, and rightly so.

So it's rather ironic that he subscribes to three discredited claims about the World Trade Center, which undermine his argument.

First, he claims that "while the number of Jews working in the WTC numbered a few thousands, less than a dozen Jews died there." This is false. "...the number of Jews who died in the attacks is variously estimated at between 270 to 400. The lower figure tracks closely with the percentage of Jews living in the New York area and partial surveys of the victims' listed religion. The U.S. State Department has published a partial list of 76 in response to claims that fewer Jews/Israelis died in the WTC attacks than should have been present at the time."

Second, he claims that "As a matter of fact more Muslims died there that day than Jews". There is no evidence in support of this claim. For example, this page of Muslim victims lists only 60, less than the partial list of 76 Jews mentioned above.

Third, he claims that Jews "were forewarned of the impending attack by an intelligence monitoring service, operating out of Israel". This is a nasty smear that cannot survive even the most cursory examination, and is debunked in the 9/11 commission report.

Yes, the backlash against the Cordoba Center is bigotry and every right-thinking person should condemn it. But publishing discredited anti-Semitic claims is also bigotry. Siddiqui should be ashamed.

Postscript: Habib Saddiqui is even worse than I thought. Compare his piece, as published in the Asian Tribune with what is apparently the the original version as published on his blog.

In the blog version, he's got the following lines: Steve Beckow is one such noble Jew who was a former Member of the Immigration and Refugee Board of Canada. He wrote an article “To Muslims of America, I Apologize." He believes that “9/11 was truly, as has been said, an "inside job." It was an engineered false-flag operation in which some Muslims played a role, but in the employ of primarily American agencies like the CIA and FBI. It featured not only some Muslims, but also some Israelis as well as nationals from many other countries.”

This looniness was apparently too much even for the Asian Tribune.

It's really pathetic that some Muslims can't own up to the fact that the WTC terrorists were Muslims organized and directed by Osama bin Laden. Crazed accusations about "false-flag operation[s]" take away every shred of credibility Siddiqui aspires to. Siddiqui should read The Looming Tower by Lawrence Wright. It leaves no doubt about who was responsible for 9/11.

Post-PostscriptI wondered what kind of person Siddiqui's source for his 9/11 allegations, Steve Beckow, was. So I wondered over to his blog, only to discover a huge fountain of woo. Beckow apparently thinks that "At an early but unknown date, we can expect a world leader (probably President Obama) to disclose the fact that human beings from other star systems are here, in spacecraft around our planet – some cloaked, some in other dimensions – and that evolved life exists in many places in the universe." Yeah, he's a real credible source. Siddiqui should be ashamed to cite this psychoceramic.

Tuesday, August 03, 2010

I occasionally visit the blog of Doug Groothuis, a Christian philosopher and intelligent design apologist. I find it a puzzle, because while many of his posts seem to be about the intellectual failings of others, he rarely bothers to provide a coherent argument himself. Instead, his blog seems to be a forum where he can enumerate his prejudices in one or two lines.

This is a typical example: Groothuis describes a presidential proclamation that "Nurturing families come in many forms, and children may be raised by a father and mother, a single father, two fathers, a step-father, a grandfather, or caring guardian" as "against all reason". But he refuses to explain why, and he also refused to publish my comment pointing this out.

Like many Christian bloggers, Groothuis routinely censors comments. About half of the things I've submitted have been rejected, with no explanations.

So I was particularly amused to see this post, which expressed Groothuis' "despair" over the "dearth of discourse". Well, if you routinely censor comments, then of course there's going to be a dearth of discourse.

So I wrote to Groothuis, as follows:

Dear Prof. Groothuis:

I'm sending you this comment via e-mail because - ironically - you do not permit comments to your posting of July 11 about comments.

In that posting you express your despair over the "dearth of discourse". I think you're wrong, and here's why:

1. Blogs typically aren't viewed in the same way as academic articles or formal debates. They're typically more like a conversation in your home. In a conversation in your home, people don't expect every utterance to be a formal presentation, and they'd probably leave rather quickly if you insisted on it. If you want a more formal setting, there are lots of opportunities, such as academic journals.

2. I'm not sure you meant "dearth", because later you say "death". But assuming "dearth" is what you meant, I see no "dearth of discourse" in blogs. On the contrary, more people are discussing more ideas than ever before, because the opportunities for discussion are greater. Just look at a newspaper site like the the NYT: in print, the NYT publishes perhaps at most 15 letters from readers a day. But on their website a single article can, and often does, result in hundreds of reader comments.

3. Your implication that discourse is worse off now than in the past is - ironically - not supported by any evidence you have presented. I'd suggest reading /American Aurora/ to see that public discourse 200 years ago suffered from many of the same problems you have pointed out.

4. Your claim that "People do not study the art of argument or the forms of fallacies" is - ironically - unsupported by any actual data. Why not present some?

5. How is a posting where you say "This is a severe attack on freedom of religion and freedom of speech", but without giving any rationale for why you think so, contributing to "discourse"? Another example is "Against all Reason - Obama endorses homosexual parenting on Father's Day." You offer no explanation why you think this is "against all reason". What kind of "discourse" is that? If you don't have time to do so, that's understandable, but then you can scarcely rail against the dearth (or death) of discourse.

The other point I'd like to make is that it's a bit rich to decry the "dearth of discourse" on the one hand and randomly shut off comments on your posts and censor commenters. If you want people to read and react to your blog, then let them. I have, on several occasions, spent half an hour or more composing what I thought was a carefully-reasoned response to your blog, only to have it not appear because it apparently violated some internal rule of yours. This is not conducive to "discourse".

Here's an extract from a stupid letter to the editor of my local newspaper, the Kitchener-Waterloo Record:

"Some of the world's leading scientists are wrestling with a number of very big, profound questions, namely: Why is there anything? Why should there be anything? How and when did living cells appear on our planet? What is the essential nature of life? What is the nature of - and relationship between - space and time? Did anything exist prior to the Big Bang about 14 billion years ago?

...

"...I rather doubt that even Stephen Hawking can imagine, or describe, a perfectly straight line that continues forever, with no beginning and no ending. To do so would be to understand infinity, which is beyond the scope of our finite minds.

"Ideally it would be great if science and good religion could work together, as partners, on these questions."

What confusion! The writer describes a "straight line that continues forever", and then says it can't be described. He also doesn't seem to know that such a line is discussed and described in the 7th grade curriculum. Nor does he seem to know that infinity, in its many variations, is routinely understood by the finite minds of mathematicians.

Then he proposes that "good religion" would be a partner for science to answer his questions. My question is, exactly what would "good religion" bring to the table?

Interviewer Tony Cox: "Do you know whether or not a gun would even operate in zero gravity?"

Roach: "Oh! You know, ahh, that's something for the Mythbusters to play around with!"

(Now, there is actually a small scientific issue about whether a gun will fire in space, but it has nothing to do with "zero gravity". A gun's firing comes from a chemical reaction, and that chemical reaction needs oxygen. In an oxygen-free environment, if the gunpowder doesn't contain its own oxidizer, the gun wouldn't fire. But, as I understand it, most modern gun cartridges do contain their own oxidizers, so this would not be an issue.)

If you don't know that "zero gravity" isn't an issue for whether a gun could fire, then you have no business writing a book about space travel.

Elsewhere in the program, Steve from Florence, Kentucky said, "I understand that when people are actually put into a Faraday cage so there's no electromagnetic radiation that actually comes in contact with them, they kind of lose the ability to actually think. As I understand it, when humans go into space, this is a problem. How has NASA dealt with this?" And instead of laughing and explaining why this is nonsense, Roach goes off onto a tangent about "space stupids".

Shouldn't a good science education be a prerequisite for science writers?

Sunday, July 11, 2010

One of the best moments in Annie Hall occurs when Alvy Singer (Woody Allen) is standing in line at the theater with Annie Hall (Diane Keaton), listening to a guy pontificate behind him. When the guy mentions Marshall McLuhan, Singer pulls out McLuhan from behind a poster, who then proceeds to say "You know nothing of my work!"

Singer then says, "Boy, if life were only like this!"

Well, perhaps what just happened to me is not up to that standard, but here goes anyway:

I wrote to Alan Sokal and asked him what he thought of DonaldM's ramblings. Here are excerpts from his e-mail to me (ellipses, as usual, denote omissions):

Many thanks for drawing my attention to that strange blog item... I don't really understand the logic of how that ID guy is purporting to use me!

I mean, I looked at Paul Greenberg's article in the Jewish World Review that he cites http://www.jewishworldreview.com/cols/greenberg070610.php3?printer_friendly and it seems to be a straightforward piece supporting my contention that there is such a thing as objective reality (though he didn't get quite correct his purported quote from me). But then the ID guy seems to overlook the obvious irony in the paragraph from Greenberg that he quotes, and takes it literally -- or else he just drops the subject there, says that "All this reminds me" of something else that is vaguely related, and goes on with his own pet story.

Now, that story makes a valid point, namely that how one interprets evidence is affected (though not determined) by the preconceptions one comes with. But if we are having a contest about who is more open to having his or her preconceptions be refuted by inconvenient evidence, then I would have to say that -- though no one is perfect -- scientists win hands down over the devotees of sacred texts. (I know, I know, they will respond in a chorus: ID is not religion, and our support for ID does not arise from any religious commitment but simply from our dispassionate analysis of the scientific evidence. Yeah, right.)

Saturday, July 03, 2010

He didn't rob a bank or run over a priest. No, his only crime was to take a photograph of one of the US's most enduring symbols of freedom: the Liberty Bell.

Back in 1942, the country was at war. My father hadn't yet enlisted in the Army; he was still a reporter for the Philadelphia Record. He was living only three blocks away from the Liberty Bell, which at the time was in Independence Hall. (Now it's in its own special building across the street.) My father often met tourists who wanted to take a picture of the Liberty Bell, but were prevented from doing so by an arbitrary rule imposed by the Bureau of City Property. My father got indignant when he learned that commercial photographers were able to take pictures of the Liberty Bell, but not the average citizen. That's the way my father was -- he liked to stick up for the little guy.

So he took a photograph -- and promptly got arrested. Maybe it was partly a publicity stunt for the newspaper, but I think he was trying to make a serious point, too. Officials asked if he was a communist, and called him "vindictive". He spent the night in jail. But after the article he wrote about his experience appeared in the Record, he was acquitted of the charge of "breach of the peace" by Magistrate Nathan A. Belfel. Maybe that's because my father was clever enough to bring along some important people, like the president of the Philadelphia Stock Exchange, to witness his arrest and speak on his behalf. Today, I'm happy to say, that old rule about the Liberty Bell is no longer in place.

But some things never change. We're at war again. And ordinary citizens are still being harassed for taking perfectly legal photographs of public buildings.

My father died in 1995. I like to think, however, that if he were still alive, he'd still be sticking up for the little guy -- and for the right to photograph without being arrested by overzealous officials.

Wednesday, June 30, 2010

Over at Uncommon Descent, Denyse O'Leary, the world's worst journalist™, gives us a list of her favorite science books --- in her usual barely literate style. (Note to Denyse: the plural of "coo" is not "coo's".)

No surprise, three of them aren't written by scientists: Darwin on Trial, Signature in the Cell, and Alfred Russel Wallace's Theory of Intelligent Evolution. Of the other two, one was written by a very mediocre scientist who made basic mistakes in previous books, and the other by a man whose bogus claims were repudiated by his own department. In Denyse's topsy-turvy world, actual scientists can be dismissed as "mooches and tax burdens", or "British aristocrats".

The late Martin Gardner studied this kind of crankery and knew how to recognize it. A scientific crank, Gardner said, "has strong compulsions to focus his attacks on the greatest scientists and the best-established theories." It is not possible to reason with this kind of idiocy -- ridicule is the best response.

Actually, Denyse's list would be a good start on a list of the Worst Science Books. Do you have any more nominations? I'll start with Judith Hooper's Of Moths and Men, Arthur Koestler's The Case of the Midwife Toad, and anything by Jeremy Rifkin.

Thursday, June 24, 2010

I recently read a fun little book, Mr. Jefferson and the Giant Moose, by Lee Alan Dugatkin. It's the story of a little-known episode in American history -- how Jefferson tried to combat the bogus claims of French naturalist Georges-Louis Leclerc, Comte de Buffon, that North American biota was "degenerate" compared to European biota.

Jefferson was worried that if such claims became accepted knowledge, then the US's reputation would suffer. Who would want to conduct trade with "degenerate" humans, or buy "degenerate" agricultural products?

In part, Buffon's claims were responsible for Jefferson's magnum opus, Notes on the State of Virginia, the most important American book published before 1800. Writing Notes involved correspondence with luminaries such as James Madison. Dugatkin quotes from a 1786 letter from Madison to Jefferson, where they discuss the fine points of weasel biology, including measuring the "width of the ears horizontally" and the "distance between the anus and the vulva".

But Jefferson had other ideas for convincing Buffon. As the book's title suggests, Jefferson's most concerted effort in terms of hands-on evidence was to procure a very large, dead, stuffed American moose - antlers and all - to hand Buffon personally in Paris, in effect saying "see".

You can't help but love a book that has sentences like "The first pre-moose incident occurred just before Jefferson was to sail off to his ministerial post in France" and "The second pre-moose instance -- wherein Jefferson encountered in Buffon a man who seemed to refuse to budge, even in the face of physical evidence -- revolved around the "mammoth" discussed in Notes on the State of Virginia."

I recommend it to anyone interested in the crucial role of ungulates in American history.

Wednesday, June 23, 2010

Mirko Petricevic, the religion reporter for the Kitchener-Waterloo Record, is at it again.

I previously criticized his coverage of a local creationist group. I pointed out that Petricevic -- unlike a good reporter -- never asks any hard questions of believers. Instead, his "reporting" is mostly just taking dictation.

Now he's got an article about the local Christian Science church, and he's employing exactly the same modus operandi: local believers are allowed to prattle on, and not a single skeptical word in the entire article.

Reading it, you would never know that there is no good evidence that prayer works to heal people of diseases. Nor would you know that Christian Science practitioners have been implicated in dozens of cases of medical neglect, where simple and safe treatment could have saved lives.

* Courtney Brown, a political scientist at Emory University who, according to Michael Shermer, is not allowed to mention his affiliation with Emory when discussing remote viewing. Did I mention that he was a "yogic flyer"?

Oh, the fun I could have had! For example, in the description of Jahn's talk, he says, "repeated applications proved to diminish the yield, suggesting that disproportionate focus on the analytical components of the perception, rather than on the phenomenal gestalt, can result in obscuring the essence of the phenomenon and that the subjective quality of these experiences is more effectively enhanced when their inherent uncertainties are both acknowledged and emphasized."

Translation: we can't figure out why our discovery of tiny psi effects disappear when we do more trials.

Saturday, June 19, 2010

This house in New England was owned by one of America's most celebrated writers. One of his lesser-known achievements was a long attack on a home-grown American religion. This writer wrote most of his celebrated works in this house.

Wednesday, June 16, 2010

I am fascinated by cranks and crank mathematics, and there's a lot of them/it out there. Here's a new "proof" of Fermat's last theorem I was sent yesterday. There is only a small amount of entertainment value in this one, with phrases such as "only one of those cofactors is organically entered into the structure of the pair of conjugate variables". Much better is the book The Life-Romance of an Algebraist by George Winslow Pierce.

The fine-structure constant α is a fundamental constant in physics, and is currently estimated to be approximately .0072973525376.

The physicist Arthur Eddington, who became rather eccentric and believed he could compute the number of protons in the universe accurately, thought it was equal to exactly 1/137, but our current estimate gives something closer to 1/137.03599967899.

The mathematician James Gilson seems to think that α is given by the rather complicated formula (29/π)*cos(π/137)*tan(π/(137*29)). But this is just numerology, and not even particularly impressive numerology. The trick is that tan(x) is very close to x when x is small, and cos(x) is very close to 1 when x is small. So Gilson's formula is just (29/π) times something that is very close to π/(137*29), with an additional fudge factor of something that's very close to 1 thrown in. There is no real surprise, then, that one can find small integers to make this close to α.

Monday, June 14, 2010

I am a graduate student in XXX University majoring in YYY. I want to cite one of your papers that should be of great use to my current research. The title of the paper is "Randomized Algorithms in Number Theory", published on Communications on Pure and Applied Mathematics 39 (1986), S1.

Because our library does not have access to the article, it should be best that you send me a copy via email.

Friday, June 11, 2010

My great-great-great-great-grandfather was John Alexander (1738-1799), a minister in the Church of England and a Loyalist during the Revolutionary War. (Although I'd have preferred a freethinker and a revolutionary, we don't get to choose our ancestors.) Here is a copy of his will, as reproduced in Volume 2, No. 4 (October 1901) of J. R. B. Hathaway's North Carolina Historical and Genealogical Register. The will is dated April 4 1795 and was probated in the August 1799 term of the court of Bertie County, North Carolina.

"Da Praecepta, Familiae, Tuae nam Tu Crive Morituruses."

"For as much as the last scene of life seems hastening on, and the curtain ready to fall," I think it prudent, before I make my final exit off the stage, whereon I have some time acted, to dispose of the few trifles fortune has bestowed me, in manner following to-wit:

Imprimis. I Give and bequeath to my two Daughters, Martha and Rachel, all and every part of my property whatever, to be equally divided between them, and to their lawful heirs forever. On the demise of either, before impowered to make a will, the surviving sister inherits the whole and should both decease, before the laws capacitate to will, then, my remaining property to be wholly converted to Educating the poor children within the counties of Hertford and Bertie; under such regulations as my Executors shall think fit. My body I bequeath to the earth, whence it originated, My Soul Immortal and unalloyed to dust, I commend to the Father of Mercies.

The manly, masculine Voice of Orthodoxy, is no longer heard in our land. Far, therefore, from my Grave be the senseless Rant of Whining Fanaticism; her hated and successful rival --- Cant and Grimace dishonour the dead, as well as Disgrace the living. Let the monitor within, who never Deceives, alone pronounce my Funeral Oration; while some Friendly hand Deposits my poor remains Close by the ashes of my beloved Daughter Elizabeth, with whom I trust to share a happy Eternity.

And of this my last Will and Testament, I constitute and appoint Capt'n George West, George Outlaw, Esq., and Mr. Edward Outlaw, my Executors, On whose Probity, Honor, and Disinterested Friendship, I entirely rely for the faithful Discharge of the trust I repose in them. Beseeching them, as they would approve themselves to him who is the Father of the Fatherless, to use all possible means of Inspiring my children with a love of Virtue and an abhorrence of Vice, Restraining them from all plans and persons Dangerous to their Virtue or Innocency --- Giving them an Education to their rank in life suitable and becoming. Let their books and their needles be their principal companions and Employ. I could wish the laws enable me to do more for my wretched and unfortunate slaves than that of recommending them to lenity and mild treatment.

Be to their faults a little blind;Be to their virtues ever kind.

JOHN ALEXANDER.

The "manly, masculine Voice of Orthodoxy" is the Church of England; the "senseless Rant of Whining Fanaticism" is either the Episcopalian Church or the Baptist Church.

I don't know why, if he found his slaves "wretched and unfortunate", he didn't just free them. But perhaps it was just so far beyond the social norm that he didn't feel it possible to do so.